Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A technician is performing measurements with very small numbers. They need to subtract 3.5 x 10^-5 from 7.2 x 10^-4. What is the result in scientific notation?
- A3.7 x 10^-5
- B6.85 x 10^-5
- C3.7 x 10^-4
- D6.85 x 10^-4
Show answer & explanationAnswer & explanation
Correct answer: D. 6.85 x 10^-4
To subtract numbers in scientific notation, their exponents must be the same. Convert 3.5 x 10^-5 to 0.35 x 10^-4. Then, subtract: (7.2 x 10^-4) - (0.35 x 10^-4) = (7.2 - 0.35) x 10^-4 = 6.85 x 10^-4.
Why the other options are wrong
- A. This results from incorrect subtraction or failure to align exponents.
- B. This results from an error in aligning exponents, likely subtracting with 10^-5 as the common exponent.
- C. This results from a direct subtraction of the mantissas without adjusting exponents.
Adding/Subtracting Scientific Notation
To add or subtract numbers in scientific notation, first adjust one or both numbers so they have the same exponent. Then, add or subtract their coefficients (mantissas) and keep the common exponent.
- Exponents must be the same before adding/subtracting
- Adjust mantissa if exponent is changed (e.g., 3.5 x 10^-5 = 0.35 x 10^-4)
- Add/subtract mantissas, keep common exponent
Memory trick: Scientific: Shift the dot, match the power, calculate.